結果

問題 No.1214 Market
ユーザー LayCurseLayCurse
提出日時 2020-08-30 17:33:23
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 150 ms / 2,000 ms
コード長 14,431 bytes
コンパイル時間 3,432 ms
コンパイル使用メモリ 224,012 KB
最終ジャッジ日時 2025-01-14 01:22:27
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 39
権限があれば一括ダウンロードができます

ソースコード

diff # 

#pragma GCC optimize ("Ofast")
#include<bits/stdc++.h>
using namespace std;
#define MD (1000000007U)
void *wmem;
char memarr[96000000];
template<class S, class T> inline S max_L(S a,T b){
  return a>=b?a:b;
}
template<class T> inline void walloc1d(T **arr, int x, void **mem = &wmem){
  static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1};
  (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] );
  (*arr)=(T*)(*mem);
  (*mem)=((*arr)+x);
}
template<class T1> void sortA_L(int N, T1 a[], void *mem = wmem){
  sort(a, a+N);
}
template<class T1, class T2> void sortA_L(int N, T1 a[], T2 b[], void *mem = wmem){
  int i;
  pair<T1, T2> *arr;
  walloc1d(&arr, N, &mem);
  for(i=(0);i<(N);i++){
    arr[i].first = a[i];
    arr[i].second = b[i];
  }
  sort(arr, arr+N);
  for(i=(0);i<(N);i++){
    a[i] = arr[i].first;
    b[i] = arr[i].second;
  }
}
template<class T1> void rsortA_L(int N, T1 a[], void *mem = wmem){
  sortA_L(N, a, mem);
  reverse(a, a+N);
}
template<class T1, class T2> void rsortA_L(int N, T1 a[], T2 b[], void *mem = wmem){
  sortA_L(N, a, b, mem);
  reverse(a, a+N);
  reverse(b, b+N);
}
struct Modint{
  unsigned val;
  Modint(){
    val=0;
  }
  Modint(int a){
    val = ord(a);
  }
  Modint(unsigned a){
    val = ord(a);
  }
  Modint(long long a){
    val = ord(a);
  }
  Modint(unsigned long long a){
    val = ord(a);
  }
  inline unsigned ord(unsigned a){
    return a%MD;
  }
  inline unsigned ord(int a){
    a %= (int)MD;
    if(a < 0){
      a += MD;
    }
    return a;
  }
  inline unsigned ord(unsigned long long a){
    return a%MD;
  }
  inline unsigned ord(long long a){
    a %= (int)MD;
    if(a < 0){
      a += MD;
    }
    return a;
  }
  inline unsigned get(){
    return val;
  }
  inline Modint &operator+=(Modint a){
    val += a.val;
    if(val >= MD){
      val -= MD;
    }
    return *this;
  }
  inline Modint &operator-=(Modint a){
    if(val < a.val){
      val = val + MD - a.val;
    }
    else{
      val -= a.val;
    }
    return *this;
  }
  inline Modint &operator*=(Modint a){
    val = ((unsigned long long)val*a.val)%MD;
    return *this;
  }
  inline Modint &operator/=(Modint a){
    return *this *= a.inverse();
  }
  inline Modint operator+(Modint a){
    return Modint(*this)+=a;
  }
  inline Modint operator-(Modint a){
    return Modint(*this)-=a;
  }
  inline Modint operator*(Modint a){
    return Modint(*this)*=a;
  }
  inline Modint operator/(Modint a){
    return Modint(*this)/=a;
  }
  inline Modint operator+(int a){
    return Modint(*this)+=Modint(a);
  }
  inline Modint operator-(int a){
    return Modint(*this)-=Modint(a);
  }
  inline Modint operator*(int a){
    return Modint(*this)*=Modint(a);
  }
  inline Modint operator/(int a){
    return Modint(*this)/=Modint(a);
  }
  inline Modint operator+(long long a){
    return Modint(*this)+=Modint(a);
  }
  inline Modint operator-(long long a){
    return Modint(*this)-=Modint(a);
  }
  inline Modint operator*(long long a){
    return Modint(*this)*=Modint(a);
  }
  inline Modint operator/(long long a){
    return Modint(*this)/=Modint(a);
  }
  inline Modint operator-(void){
    Modint res;
    if(val){
      res.val=MD-val;
    }
    else{
      res.val=0;
    }
    return res;
  }
  inline operator bool(void){
    return val!=0;
  }
  inline operator int(void){
    return get();
  }
  inline operator long long(void){
    return get();
  }
  inline Modint inverse(){
    int a = val;
    int b = MD;
    int u = 1;
    int v = 0;
    int t;
    Modint res;
    while(b){
      t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    if(u < 0){
      u += MD;
    }
    res.val = u;
    return res;
  }
  inline Modint pw(unsigned long long b){
    Modint a(*this);
    Modint res;
    res.val = 1;
    while(b){
      if(b&1){
        res *= a;
      }
      b >>= 1;
      a *= a;
    }
    return res;
  }
  inline bool operator==(int a){
    return ord(a)==val;
  }
  inline bool operator!=(int a){
    return ord(a)!=val;
  }
}
;
inline Modint operator+(int a, Modint b){
  return Modint(a)+=b;
}
inline Modint operator-(int a, Modint b){
  return Modint(a)-=b;
}
inline Modint operator*(int a, Modint b){
  return Modint(a)*=b;
}
inline Modint operator/(int a, Modint b){
  return Modint(a)/=b;
}
inline Modint operator+(long long a, Modint b){
  return Modint(a)+=b;
}
inline Modint operator-(long long a, Modint b){
  return Modint(a)-=b;
}
inline Modint operator*(long long a, Modint b){
  return Modint(a)*=b;
}
inline Modint operator/(long long a, Modint b){
  return Modint(a)/=b;
}
inline int my_getchar_unlocked(){
  static char buf[1048576];
  static int s = 1048576;
  static int e = 1048576;
  if(s == e && e == 1048576){
    e = fread_unlocked(buf, 1, 1048576, stdin);
    s = 0;
  }
  if(s == e){
    return EOF;
  }
  return buf[s++];
}
inline void rd(int &x){
  int k;
  int m=0;
  x=0;
  for(;;){
    k = my_getchar_unlocked();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = my_getchar_unlocked();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
struct MY_WRITER{
  char buf[1048576];
  int s;
  int e;
  MY_WRITER(){
    s = 0;
    e = 1048576;
  }
  ~MY_WRITER(){
    if(s){
      fwrite_unlocked(buf, 1, s, stdout);
    }
  }
}
;
MY_WRITER MY_WRITER_VAR;
void my_putchar_unlocked(int a){
  if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){
    fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout);
    MY_WRITER_VAR.s = 0;
  }
  MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a;
}
inline void wt_L(char a){
  my_putchar_unlocked(a);
}
inline void wt_L(int x){
  int s=0;
  int m=0;
  char f[10];
  if(x<0){
    m=1;
    x=-x;
  }
  while(x){
    f[s++]=x%10;
    x/=10;
  }
  if(!s){
    f[s++]=0;
  }
  if(m){
    my_putchar_unlocked('-');
  }
  while(s--){
    my_putchar_unlocked(f[s]+'0');
  }
}
inline void wt_L(Modint x){
  int i;
  i = (int)x;
  wt_L(i);
}
template<class T, class S> inline T pow_L(T a, S b){
  T res = 1;
  res = 1;
  for(;;){
    if(b&1){
      res *= a;
    }
    b >>= 1;
    if(b==0){
      break;
    }
    a *= a;
  }
  return res;
}
inline double pow_L(double a, double b){
  return pow(a,b);
}
template<class S> inline void arrInsert(const int k, int &sz, S a[], const S aval){
  int i;
  sz++;
  for(i=sz-1;i>k;i--){
    a[i] = a[i-1];
  }
  a[k] = aval;
}
template<class S, class T> inline void arrInsert(const int k, int &sz, S a[], const S aval, T b[], const T bval){
  int i;
  sz++;
  for(i=sz-1;i>k;i--){
    a[i] = a[i-1];
  }
  for(i=sz-1;i>k;i--){
    b[i] = b[i-1];
  }
  a[k] = aval;
  b[k] = bval;
}
template<class S, class T, class U> inline void arrInsert(const int k, int &sz, S a[], const S aval, T b[], const T bval, U c[], const U cval){
  int i;
  sz++;
  for(i=sz-1;i>k;i--){
    a[i] = a[i-1];
  }
  for(i=sz-1;i>k;i--){
    b[i] = b[i-1];
  }
  for(i=sz-1;i>k;i--){
    c[i] = c[i-1];
  }
  a[k] = aval;
  b[k] = bval;
  c[k] = cval;
}
template<class S, class T, class U, class V> inline void arrInsert(const int k, int &sz, S a[], const S aval, T b[], const T bval, U c[], const U cval, V d[], const V dval){
  int i;
  sz++;
  for(i=sz-1;i>k;i--){
    a[i] = a[i-1];
  }
  for(i=sz-1;i>k;i--){
    b[i] = b[i-1];
  }
  for(i=sz-1;i>k;i--){
    c[i] = c[i-1];
  }
  for(i=sz-1;i>k;i--){
    d[i] = d[i-1];
  }
  a[k] = aval;
  b[k] = bval;
  c[k] = cval;
  d[k] = dval;
}
template<class S, class T> inline S chmax(S &a, T b){
  if(a<b){
    a=b;
  }
  return a;
}
template<class T> struct Comb{
  int mem_fact;
  T *factri;
  T *ifactri;
  Comb(){
    mem_fact = 0;
  }
  inline void expand_fact(int k){
    if(k <= mem_fact){
      return;
    }
    chmax(k, 2* mem_fact);
    if(mem_fact == 0){
      int i;
      factri = (T*)malloc(k * sizeof(T));
      ifactri = (T*)malloc(k * sizeof(T));
      factri[0] = 1;
      for(i=(1);i<(k);i++){
        factri[i] = i * factri[i-1];
      }
      ifactri[k-1] = 1 / factri[k-1];
      for(i=(k-1)-1;i>=(0);i--){
        ifactri[i] = (i+1) * ifactri[i+1];
      }
    }
    else{
      int i;
      factri = (T*)realloc(factri, k * sizeof(T));
      ifactri = (T*)realloc(ifactri, k * sizeof(T));
      for(i=(mem_fact);i<(k);i++){
        factri[i] = i * factri[i-1];
      }
      ifactri[k-1] = 1 / factri[k-1];
      for(i=(k-1)-1;i>=(mem_fact);i--){
        ifactri[i] = (i+1) * ifactri[i+1];
      }
    }
    mem_fact = k;
  }
  inline T fac(int k){
    if(mem_fact < k+1){
      expand_fact(k+1);
    }
    return factri[k];
  }
  inline T ifac(int k){
    if(mem_fact < k+1){
      expand_fact(k+1);
    }
    return ifactri[k];
  }
  inline T C(int a, int b){
    if(b < 0 || b > a){
      return 0;
    }
    if(mem_fact < a+1){
      expand_fact(a+1);
    }
    return factri[a] * ifactri[b] * ifactri[a-b];
  }
  inline T P(int a, int b){
    if(b < 0 || b > a){
      return 0;
    }
    if(mem_fact < a+1){
      expand_fact(a+1);
    }
    return factri[a] * ifactri[a-b];
  }
  inline T H(int a, int b){
    if(a==0 && b==0){
      return 1;
    }
    if(a <= 0 || b < 0){
      return 0;
    }
    if(mem_fact < a+b){
      expand_fact(a+b);
    }
    return C(a+b-1, b);
  }
  inline T Multinomial(int sz, int a[]){
    int i;
    int s = 0;
    T res;
    for(i=(0);i<(sz);i++){
      s += a[i];
    }
    if(mem_fact < s+1){
      expand_fact(s+1);
    }
    res = factri[s];
    for(i=(0);i<(sz);i++){
      res *= ifactri[a[i]];
    }
    return 1;
  }
  inline T Multinomial(int a){
    return 1;
  }
  inline T Multinomial(int a, int b){
    if(mem_fact < a+b+1){
      expand_fact(a+b+1);
    }
    return factri[a+b] * ifactri[a] * ifactri[b];
  }
  inline T Multinomial(int a, int b, int c){
    if(mem_fact < a+b+c+1){
      expand_fact(a+b+c+1);
    }
    return factri[a+b+c] * ifactri[a] * ifactri[b] * ifactri[c];
  }
  inline T Multinomial(int a, int b, int c, int d){
    if(mem_fact < a+b+c+d+1){
      expand_fact(a+b+c+d+1);
    }
    return factri[a+b+c+d] * ifactri[a] * ifactri[b] * ifactri[c] * ifactri[d];
  }
  inline T Catalan(int n){
    if(n < 0){
      return 0;
    }
    if(mem_fact < 2*n+1){
      expand_fact(2*n+1);
    }
    return factri[2*n] * ifactri[n] * ifactri[n+1];
  }
  inline T C_s(long long a, long long b){
    long long i;
    T res;
    if(b < 0 || b > a){
      return 0;
    }
    if(b > a - b){
      b = a - b;
    }
    res = 1;
    for(i=(0);i<(b);i++){
      res *= a - i;
      res /= i + 1;
    }
    return res;
  }
  inline T P_s(long long a, long long b){
    long long i;
    T res;
    if(b < 0 || b > a){
      return 0;
    }
    res = 1;
    for(i=(0);i<(b);i++){
      res *= a - i;
    }
    return res;
  }
  inline T per_s(long long n, long long k){
    T d;
    int m;
    if(n < 0 || k < 0){
      return 0;
    }
    if(n == k  &&  k == 0){
      return 1;
    }
    if(n == 0 || k == 0){
      return 0;
    }
    if(k==1){
      return 1;
    }
    if(k==2){
      d = n / 2;
      return d;
    }
    if(k==3){
      d = (n-1) / 6;
      m = (n-1) % 6;
      if(m==0){
        return 3 * d * d + d;
      }
      if(m==1){
        return 3 * d * d + 2 * d;
      }
      if(m==2){
        return 3 * d * d + 3 * d + 1;
      }
      if(m==3){
        return 3 * d * d + 4 * d + 1;
      }
      if(m==4){
        return 3 * d * d + 5 * d + 2;
      }
      if(m==5){
        return 3 * d * d + 6 * d + 3;
      }
    }
    assert(0 && "per_s should be k <= 3");
    return -1;
  }
}
;
int N;
int M;
int K;
int A[40];
int B[40];
Modint dp[41][41];
Modint nx[41][41];
Comb<Modint> c;
Modint solve(int N, int M, int A[], int tar[]){
  int i, k;
  int f = 0;
  Modint res = 0;
  Modint p;
  rsortA_L(M, A, tar);
  for(i=(0);i<(N+1);i++){
    int j;
    for(j=(0);j<(N+1);j++){
      dp[i][j] = 0;
    }
  }
  dp[N][0] = 1;
  for(k=(0);k<(M);k++){
    f += tar[k];
    if(k==0){
      p = Modint(K - A[k] + 1) / (K+1);
    }
    else{
      p = Modint(A[k-1] - A[k]) / A[k-1];
    }
    for(i=(0);i<(N+1);i++){
      int j;
      for(j=(0);j<(N+1);j++){
        nx[i][j] = 0;
      }
    }
    for(i=(0);i<(N+1);i++){
      int j;
      for(j=(0);j<(N+1);j++){
        if((int)dp[i][j] != 0){
          int x;
          for(x=(0);x<(i+1);x++){
            if(f && j+x-1 < 0){
              continue;
            }
            nx[i-x][max_L(0, j+x-1)] += dp[i][j] * c.C(i,x) * ((pow_L(p,x))) * ((pow_L((1-p),(i-x))));
          }
        }
      }
    }
    for(i=(0);i<(N+1);i++){
      int j;
      for(j=(0);j<(N+1);j++){
        dp[i][j] = nx[i][j];
      }
    }
  }
  for(i=(0);i<(N+1);i++){
    int j;
    for(j=(0);j<(N+1);j++){
      res += dp[i][j];
    }
  }
  return res;
}
int main(){
  int i;
  wmem = memarr;
  int nn;
  int a[40];
  int t[40];
  Modint res = 0;
  rd(N);
  rd(M);
  rd(K);
  {
    int BUotOFBp;
    for(BUotOFBp=(0);BUotOFBp<(M);BUotOFBp++){
      rd(A[BUotOFBp]);
      rd(B[BUotOFBp]);
    }
  }
  for(i=(0);i<(M);i++){
    int j;
    nn = 0;
    for(j=(0);j<(M);j++){
      if(B[j] > B[i]){
        arrInsert(nn, nn, a, A[j], t, 0);
      }
    }
    arrInsert(nn, nn, a, A[i], t, 1);
    res += solve(N, nn, a, t) * B[i];
  }
  wt_L(res);
  wt_L('\n');
  return 0;
}
// cLay varsion 20200813-1 [beta]

// --- original code ---
// int N, M, K, A[40], B[40];
// 
// Modint dp[41][41], nx[41][41];
// Comb<Modint> c;
// 
// Modint solve(int N, int M, int A[], int tar[]){
//   int f = 0;
//   Modint res = 0, p;
// 
//   rsortA(M, A, tar);
//   rep(i,N+1) rep(j,N+1) dp[i][j] = 0;
//   dp[N][0] = 1;
// 
//   rep(k,M){
//     f += tar[k];
// 
//     if(k==0) p = Modint(K - A[k] + 1) / (K+1);
//     else     p = Modint(A[k-1] - A[k]) / A[k-1];
// 
//     rep(i,N+1) rep(j,N+1) nx[i][j] = 0;
// 
//     rep(i,N+1) rep(j,N+1) if((int)dp[i][j] != 0){
//       rep(x,i+1){
//         if(f && j+x-1 < 0) continue;
//         nx[i-x][max(0,j+x-1)] += dp[i][j] * c.C(i,x) * (p ** x) * ((1-p) ** (i-x));
//       }
//     }
// 
//     rep(i,N+1) rep(j,N+1) dp[i][j] = nx[i][j];
//   }
// 
//   rep(i,N+1) rep(j,N+1) res += dp[i][j];
//   return res;
// }
// 
// {
//   int nn, a[40], t[40];
//   Modint res = 0;
//   rd(N,M,K,(A,B)(M));
//   rep(i,M){
//     nn = 0;
//     rep(j,M) if(B[j] > B[i]) arrInsert(nn, nn, a, A[j], t, 0);
//     arrInsert(nn, nn, a, A[i], t, 1);
//     res += solve(N, nn, a, t) * B[i];
//   }
//   wt(res);
// }
0